Basic microstrip resonator question

This paper, in addition to many others, have used a half-wave resonator as a generic model used towards completion of whatever goal.

For anyone who can't view the paper, it pictures a gap-coupled half-wave resonator with feed lines much narrower than the resonating patch.

The question I have is, what is the purpose of narrower, higher impedance gap-coupled feed lines, coupled to the wider, lower impedance half-wave patch resonator? I understand the point of gap-coupling is to weakly-couple the resonator with other elements of the circuit, thereby increasing Q-factor, but which not use a microstrip patch of the same width and impedance as the feed lines?

Is the transition from higher to lower impedance to increase the magnitude of S11?

bump. Just in case it was missed the first time. If I need to clarify anything, let me know.